zbMATH — the first resource for mathematics

Transition from ciliary to flapping mode in a swimming mollusc: Flapping flight as a bifurcation in \(Re_\omega\). (English) Zbl 1059.76081
From the summary: From observations of swimming of the shell-less pteropod mollusc Clione antarctica we compare swimming velocities achieved by the organism using ciliated surfaces alone with velocities achieved by the same organism using a pair of flapping wings. Flapping dominates locomotion above a swimming Reynolds number \(Re\) in the range 5–20. We test the hypothesis that \(Re\approx 5-20\) marks the onset of ‘flapping flight’ in these organisms. We consider the proposition that forward, reciprocal flapping flight is impossible for locomoting organisms whose motion is fully determined by a body length \(L\) and a frequency \(\omega\) below some finite critical value of the Reynolds number \(Re_\omega=\omega L^2/\nu\). For a self-similar family of body shapes, the critical Reynolds number should depend only upon the geometry of the body and the cyclic movement used to locomote. We give evidence of such a critical Reynolds number in our data, and study the bifurcation in several simplified theoretical models.

76Z10 Biopropulsion in water and in air
92C10 Biomechanics
Full Text: DOI